Mladen Dimitrov

On the eigencurve at classical weight 1 points

We show that the p-adic Eigencurve is smooth at classical weight one points which are regular at p and give a precise criterion for etaleness over the weight space at those points. Our approach uses deformations of Galois representations.

Automorphic symbols, p-adic L-functions and ordinary cohomology of Hilbert modular varieties

We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general

Elliptic curves, Hilbert modular forms and Galois deformations

p

Arithmetic Aspects of Hilbert Modular Forms and Varieties

-adic

p-adic L-functions for Hilbert modular forms

L

Galois representations modulo p and cohomology of Hilbert modular varieties

-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the

On Ihara’s lemma for Hilbert modular varieties

p

On classical weight one forms in Hida families

-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ideal of the Hecke algebra. We also show its freeness over the corresponding Hecke algebra which turns out to be a universal deformation ring. In the last part of the paper we combine the above results to construct

Explicit determination of images of Galois representations attached to Hilbert modular forms

p

Test vectors for trilinear forms when at least one representation is not supercuspidal

-adic